Swaps
Chapter 26
Financial Institutions Management, 3/e
By Anthony Saunders
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Introduction
Market for swaps has grown enormously
 Serious regulatory concerns regarding credit risk
exposures

• Motivated BIS risk-based capital reforms
• Growth in exotic swaps such as inverse floater
generated controversy (e.g., Orange County, CA).

Generic swaps in order of quantitative
importance: interest rate, currency, commodity.
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Interest Rate Swaps

Interest rate swap as succession of forwards.
• Swap buyer agrees to pay fixed-rate
• Swap seller agrees to pay floating-rate.

Purpose of swap
• Allows FIs to economically convert variablerate instruments into fixed-rate (or vice versa)
in order to better match assets and liabilities.
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Interest Rate Swap Example
• Consider money center bank that has raised $100
million by issuing 4-year notes with 10% fixed
coupons. On asset side: C&I loans linked to
LIBOR. Duration gap is negative.
DA - kDL < 0
• Second party is savings bank with $100 million in
fixed-rate mortgages of long duration funded with
CDs having duration of 1 year.
DA - kDL > 0
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Example (continued)
• Savings bank can reduce duration gap by
buying a swap (taking fixed-payment side).
• Notional value of the swap is $100 million.
• Maturity is 4 years with 10% fixed-payments.
• Suppose that LIBOR currently equals 8% and
bank agrees to pay LIBOR + 2%.
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Realized Cash Flows on Swap

Suppose realized rates are as follows
End of Year
LIBOR
1
9%
2
9%
3
7%
4
6%
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Swap Payments
End of
Year
1
2
3
4
Total
LIBOR
+ 2%
11%
11
9
8
MCB
Payment
$11
11
9
8
39
Savings
Bank
$10
10
10
10
40
Net
+1
+1
-1
-2
-1
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Off-market Swaps

Swaps can be molded to suit needs
• Special interest terms
• Varying notional value
» Increasing or decreasing over life of swap.
• Structured-note inverse floater
» Example: Government agency issues note with
coupon equal to 7 percent minus LIBOR and
converts it into a LIBOR liability through a swap.
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Macrohedging with Swaps

Assume a thrift has positive gap such that
DE = -(DA - kDL)A [DR/(1+R)] >0 if rates rise.
Suppose choose to hedge with 10-year swaps. Fixedrate payments are equivalent to payments on a 10year T-bond. Floating-rate payments repriced to
LIBOR every year. Changes in swap value DS,
depend on duration difference (D10 - D1).
DS = -(DFixed - DFloat) × NS × [DR/(1+R)]
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Macrohedging (continued)

Optimal notional value requires
DS = DE
-(DFixed - DFloat) × NS × [DR/(1+R)]
= -(DA - kDL) × A × [DR/(1+R)]
NS = [(DA - kDL) × A]/(DFixed - DFloat)
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Pricing an Interest Rate Swap

Example:
• Assume 4-year swap with fixed payments at
end of year.
• We derive expected one-year rates from the
yield curve treating the individual payments as
separate zero-coupon bonds and iterating
forward.
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Currency Swaps

Fixed-Fixed
• Example: U.S. bank with fixed-rate assets
denominated in dollars, partly financed with
£50 million in 4-year 10 percent (fixed) notes.
By comparison, U.K. bank has assets partly
funded by $100 million 4-year 10 percent
notes.
• Solution: Enter into currency swap.

Fixed-Floating currency swaps.
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Credit Swaps
Credit swaps designed to hedge credit risk.
 Total return swap
 Pure credit swap

• Interest-rate sensitive element stripped out
leaving only the credit risk.
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Credit Risk Concerns
Credit risk concerns partly mitigated by
netting of swap payments.
 Netting by novation

• When there are many contracts between parties.
Payment flows are interest and not
principal.
 Standby letters of credit may be required.

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